Try meow cosmetics...they are an online cosmetics company, and you can also buy cheap sample sizes to make sure their products don't break you out. They have a decent primer for oily skin that you can wear on its own, and they only use a few ingredients to minimize chances of breaking out.

Fyrinnae is another natural company with natural ingredients. If you want to try something in stores, maybe try the Tarte amazonian clay finishing powder, which is supposed to actually improve the texture of your skin but one of the ingredients is not very healthy. I used it a few times and it didn't break me out.